Once we obtain the optimal \(\lbrace \mathbf {o}_s,\mathbf {f}_s\rbrace \) , we update \(\lbrace \mathbf {o}_s^{m+1},\mathbf {f}_s^{m+1}\rbrace \) . We alternatively minimize with respect to \(\lbrace \mathbf {g}_s,\mathbf {t}_s\rbrace \)  and \(\lbrace \mathbf {o}_s,\mathbf {f}_s\rbrace \) . Then, we update Lagrange multipliers as \(\iota ^{m+1}=\iota ^{m}+\rho _{11}(\mathbf {o}^{m+1} - \mathbf {g}^{m+1})\)  and \(\lambda ^{m+1}=\lambda ^{m}+\rho _{12}(\mathbf {f}^{m+1} - \mathbf {t}^{m+1})\) . The summary of the proposed approach to solve (REF ) is given in Algorithm REF . After Algorithm REF  converges (the primal and dual residuals are small enough, see [1]}), we use obtained \(\mathbf {g}\)  to update \(\mathbf {g}^{\pi +1}\) .
